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Bivalent Range

If the cross ratio kappa of {AB,CD} satisfy

kappa^2-kappa+1=0,
(1)

then the points are said to form a bivalent range, and

{AB,CD}={AC,DB}={AD,BC}=kappa
(2)
{AC,BD}={AD,BC}={AB,DC}=-kappa^2.
(3)

See also

Harmonic Range

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References

Lachlan, R. An Elementary Treatise on Modern Pure Geometry. London, England: Macmillian, p. 268, 1893.

Referenced on Wolfram|Alpha

Bivalent Range

Cite this as:

Weisstein, Eric W. "Bivalent Range." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/BivalentRange.html

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